English

Complexity and invariant measure of the period-doubling subshift

Dynamical Systems 2019-02-25 v1

Abstract

Explicit formulas for complexity and unique invariant measure of the period-doubling subshift can be derived from those for the Thue-Morse subshift, obtained by Brlek, De Luca and Varricchio, and Dekking. In this note we give direct proofs based on combinatorial properties of the period-doubling sequence. We also derive explicit formulas for correlation integral and other recurrence characteristics of the period-doubling subshift. As a corollary we obtain that the determinism of this subshift converges to 1 as the distance threshold approaches 0.

Keywords

Cite

@article{arxiv.1902.08387,
  title  = {Complexity and invariant measure of the period-doubling subshift},
  author = {Miroslava Poláková},
  journal= {arXiv preprint arXiv:1902.08387},
  year   = {2019}
}